Two waves of the same amplitude and wavelength travel in opposite directions along a…

PHYSICS · Single correct · CBSE · Physics · Waves · Waves

Problem

Two waves of the same amplitude

3\,\text{cm}

and wavelength

\lambda

travel in opposite directions along a string. They are given by

y_1 = 3 \sin(kx - \omega t)

and

y_2 = 3 \sin\bigl(kx + \omega t + \dfrac{\pi}{3}\bigr)

, where

k = \dfrac{2\pi}{\lambda}

. Which of the following expressions represents the resultant displacement

y(x,t)

? (a)

y = 6 \sin\left(kx + \dfrac{\pi}{6}\right) \cos\left(\omega t - \dfrac{\pi}{6}\right)

(b)

y = 6 \sin(kx) \cos\left(\omega t + \dfrac{\pi}{3}\right)

(c)

y = 6 \sin\left(kx + \dfrac{\pi}{6}\right) \cos\left(\omega t + \dfrac{\pi}{6}\right)

(d)

y = 3 \sin\left(kx + \dfrac{\pi}{6}\right) \cos\left(\omega t + \dfrac{\pi}{6}\right)